UFA Analysis

Author

Teemu Säilynoja

Published

March 21, 2025

Modified

March 26, 2025

This post got inspired by the publication of a dataset containing details on 290826 passes from 574 games, played during the 2021 to 2024 seasons of the professional league by Ultimate Frisbee Association (UFA). The dataset was published together with a 2025 sports analytics paper on estimating player value and decision making in ultimate frisbee, by Eberhard, Miller, and Sandholz.

I have often wondered how much does a good pull actually affect the offense, and celebrated when an opponent takes a timeout, as the most likely pass for the offense to lose possession is right after a time out. With this dataset, I can put some numbers behind these questions and claims!

Effect of pulls

Figure 1: How I classified the pull results for this analysis.

The dataset contains 23225 played points. Of these, 5251 start with the offense on the brick mark, or further on the field. That is, 22.6% of the offenses in the dataset started from the brick mark, or closer to the opposing end-zone.

But did the offense benefit from these bad pulls, and what about the effect of the very good pulls?

A good pull is noticeably more likely to result in a break.
Pull result	Offense held (%)	Num. points
Good	61.2	3287
OK	66.7	14687
Brick	68.5	1699
Failed	69.5	3552

Above, I consider a good pull to heightinside the end-zonwidthither of the horizontal quarters closest to the sideline. If the pull doesn’t make it past the brick mark, I mark it as a failed one. On average, good pulls seem to result in 19% more breaks. A mediocre pull does not fare much better than a bricked one, so as long as the pull gets past the brick mark, it seems to be worth it to go for the corners!

Although, even the effect of nailing every pull in a match is quite small; 1.15 extra breaks per the average 19 defense points played per match, but often¹ that one break is all your team needs.

¹ Of the recorded matches, 20% ended in a score difference of one.

--- title: "UFA Analysis" author: "Teemu Säilynoja" date: 2025/03/21 date-modified: today format: html: code-tools: true toc-title: " " reference-location: margin citation-location: margin execute: warning: false message: false echo: false cache: true knitr: opts_chunk: dev: svg dev.args: { bg: "transparent" } fig.path: ./figures/ --- ```{r} #| label: imports #| cache: false library(dplyr) library(ggplot2) library(knitr) library(kableExtra) palette <- list( red = "#bf616a", orange = "#d08770", yellow = "#ebcb8b", green = "#a3be8c", purple = "#b48ead", lblue = "#88c0d0", dblue = "#81a1c1", white = "#d8dee9", black = "#3b4252", gray = "#8699bb" ) ``` ```{r} #| label: data_loading full_data <- read.csv2("data/all_games_1024.csv", sep = ",") |> mutate(across( everything(), .fns = \(x) type.convert(x, as.is = TRUE) )) |> mutate( is_home_team = is_home_team == "True" ) ``` This post got inspired by the publication of a dataset containing details on `r nrow(full_data)` passes from `r length(unique(full_data$gameID))` games, played during the 2021 to 2024 seasons of the professional league by Ultimate Frisbee Association (UFA). The dataset was published together with a 2025 sports analytics paper on [estimating player value and decision making in ultimate frisbee](https://www.sloansportsconference.com/research-papers/a-machine-learnin g-approach-to-throw-value-estimation-in-professional-ultimate-frisbee), by Eberhard, Miller, and Sandholz. I have often wondered *how much does a good pull actually affect the offense*, and celebrated when an opponent takes a timeout, as *the most likely pass for the offense to lose possession is right after a time out*. With this dataset, I can put some numbers behind these questions and claims! ## Effect of pulls ```{r} #| label: pulls_data pulls <- full_data |> group_by( gameID, total_points, game_quarter ) |> summarise( start_type = { if (thrower_x[1] == 0 & thrower_y[1] == 40) { "Brick" } else if ((abs(thrower_x[1]) > 15 & thrower_y[1] < 15) | thrower_y[1] < 7) { "Good" } else if (thrower_y[1] < 40) { "OK" } else { "Failed" } }, is_offense_goal = { (is_home_team[1] == tail(is_home_team, 1)) & tail(receiver_y,1) > 100 }, x = thrower_x[1], y = thrower_y[1], .groups = "drop") ``` ```{r} #| label: fig-pull-results #| cache: false #| fig-height: 16 #| fig-width: 8 #| fig-cap: How I classified the pull results for this analysis. #| column: margin ggplot(pulls) + geom_tile( aes(x = 0, y = c(10, 110, 60), height = c(20, 20, 80), width = 54), data = data.frame(), fill = palette$green, color = palette$white, linewidth = 2 ) + geom_point( aes(x, y, color = factor(start_type, levels = c("Good", "OK", "Brick", "Failed")), size = I(ifelse(start_type == "Brick", 4, 2))), alpha = .5 ) + coord_equal(xlim = c(-27.5, 27.5), ylim = c(-0.5,120.5), expand = FALSE) + theme_void(base_family="sans") + theme( legend.position = "bottom", legend.text = element_text(colour = palette$gray, size = 28), legend.title = element_text(colour = palette$gray, size = 32)) + scale_color_manual( values = c("Good" = palette$yellow, "OK" = palette$orange, "Brick" = palette$lblue, "Failed" = palette$red) ) + guides( color = guide_legend(override.aes = list(size = 5, alpha = 1)), size = "none" ) + labs(color = "Pull result: ") ``` The dataset contains `r nrow(pulls)` played points. Of these, `r sum( pulls$start_type %in% c("Brick", "Failed"))` start with the offense on the brick mark, or further on the field. That is, **`r round(100 * mean(pulls$start_type %in% c("Brick", "Failed")), 1)`% of the offenses in the dataset started from the brick mark, or closer to the opposing end-zone**. But did the offense benefit from these bad pulls, and what about the effect of the very good pulls? ```{r} pull_results <- pulls |> group_by(start_type) |> summarise( offense_scoring_rate = round(100 * mean(is_offense_goal), 1), n = n() ) pull_results[c(3,4,1,2), ] |> kbl( digits = 2, label = NA, col.names = c("Pull result", "Offense held (%)", "Num. points"), table.attr = 'data-quarto-disable-processing="true"', caption = "A good pull is noticeably more likely to result in a break." ) |> kable_styling(full_width = FALSE) ``` Above, I consider a good pull to heightinside the end-zonwidthither of the horizontal quarters closest to the sideline. If the pull doesn't make it past the brick mark, I mark it as a failed one. On average, good pulls seem to result in `r 100 * round( ( mean(pulls[pulls$start_type != "Good", ]$is_offense_goal) - mean(pulls[pulls$start_type == "Good", ]$is_offense_goal) ) / ( 1 - mean(pulls[pulls$start_type != "Good", ]$is_offense_goal) ),2)`% more breaks. A mediocre pull does not fare much better than a bricked one, so as long as the pull gets past the brick mark, it seems to be worth it to go for the corners! Although, even the effect of nailing ***every*** pull in a match is quite small; `r round( (full_data |> group_by(gameID) |> reframe(points = c(tail(home_team_score,1), tail(away_team_score, 1))) |> pull(points) |> mean() ) * ( mean(pulls[pulls$start_type != "Good", ]$is_offense_goal) - mean(pulls[pulls$start_type == "Good", ]$is_offense_goal) ), 2) ` extra breaks per the average `r round(full_data |> group_by(gameID) |> reframe(points = c(tail(home_team_score,1), tail(away_team_score, 1))) |> pull(points) |> mean(), 0)` defense points played per match, but often^[Of the recorded matches, `r 100 * round( full_data |> group_by(gameID) |> summarise(score_diff_one = abs(tail(score_diff, 1)) == 1) |> pull(score_diff_one) |> mean(), 1 )`% ended in a score difference of one.] that one break is all your team needs.